1. Suppose that you generate 20 random samples from the integers {0,1, ...,9}. What are themean and variance for the number of integers that do not appear in the 20 samples?2. Let X be a Poisson random variable with parameter 2. Show directly (i.e. don't use themoment generating functions) that E[X"] = AE[(X + 1)"=1). Use the result to computeE[X®].3. Recall (from HW5) the hazard rate:fx(x)hx(x) =%3D1– Fx(x)'Suppose that X is a continuous random variable with densityfx(x) = ade-* + (1 – a)µe¬#x, for x 20for 0 < a <1 and 0<2< µ. X is then called a mixture density. Compute the hazard ratehx(x) and show that lim hx(x) = 2.

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1. Suppose that you generate 20 random samples from the integers {0,1, ., 9}. What are the mean and variance for the number of integers that do not appear in the 20 samples?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

1. Suppose that you generate 20 random samples from the integers {0,1, ...,9}. What are the
mean and variance for the number of integers that do not appear in the 20 samples?
2. Let X be a Poisson random variable with parameter 2. Show directly (i.e. don't use the
moment generating functions) that E[X"] = AE[(X + 1)"=1). Use the result to compute
E[X®].
3. Recall (from HW5) the hazard rate:
fx(x)
hx(x) =
%3D
1– Fx(x)'
Suppose that X is a continuous random variable with density
fx(x) = ade-* + (1 – a)µe¬#x, for x 20
for 0 < a <1 and 0<2< µ. X is then called a mixture density. Compute the hazard rate
hx(x) and show that lim hx(x) = 2.

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